monogon

Noun

monogon (plural monogons)

1. A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.
   • A geodesic with multiple points contains at least one simple monogon.1955, Herbert Busemann, The Geometry of Geodesics, page 295
   • There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.1981, Harold Abelson, Andrea A. DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics, →ISBN, page 262
2. A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge.
   • According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s#43;2 edges, and 4s#43;2 faces. Of these faces, 4s#43;1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.1987, Jonathan L. Gross, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231
   • There is no monogon in M-int(N(B)), ie, no disk D⊂M-int(N(B)) with ∂D=D∩N(B)=α∪β, where α⊂∂_(vN)(B) is in an interval fiber of ∂_(vN)(B) and β⊂∂_(hN)(B).2002, Tao Li, "Laminar Branched Surfaces in 3–manifolds", Geometry & Topology 6, page 158
3. A single-faceted reflector.
   • A new optical scanner is described which serves as a monogon or single-facet device, providing one scan per shaft rotation.1991, Beam Deflection, Scanning Technologies, edited by Gerald F. Marshall, Leo Beiser, →ISBN, page 33
   • These devices also start with the monogon, a plane mirror, and include the bigon, a two-sided mirror, the trigon, quadrigon, and general n-gons.1999, William L. Wolfe, Infrared Design Examples, Tutorial Texts in Optical Engineering Volume TT36, SPIE Press, →ISBN, page 133